If your projector honestly looks better than your TV, I'd be interested to know their respective model names, what kind of screen you use, how old the projection lamp is, etc.

As much as I'm a big fan of projection, I just realized that my TV currently looks so much better than my projector. In my room I put my LCD TV below my projected image, so I can readily compare the quality difference between them. Even though I only do my viewing at night, the TV (a 3 year old Toshiba 46" LCD) obviously looks better than the projected image (from a BenQ W1000+ with about 1000 hours) in every way: sharpness, color, brightness, resolution. I don't remember if it was always this way or is it because of decreased brightness due to lamp aging. Since my white wall is my screen, it was probably always inferior, although in the past I remember perceiving the projector's quality as good when it was new.

I would love for my projector to at least come close to the TV's quality, if not exceed it.

Make your image from the projector 46" and see how it compares.
You need a real screen, black ceiling, sidewalls at least 5' out and sufficient light from the projector to produce a 12fl image off the screen. What is your screen size, how far do you sit?
you have 1920x1080 Pixels make those fit in a 46" diag screen they will be very tiny and make a sharp image. Now put them on 110" screen they will be almost 1/6" in size so if you are to close it won't look as good.

My 110" image on a Dalite HP 2.8 Gain screen from a Planar 8150 looks better than my 2012 Samsung 46" TV from 13' away. What looks better it is 110" sharp as a tack with perfect color and 20+fl I have also treated the ceiling and walls when in use.. see below image in signiture
There is a lot more to getting a projected image to look correct then just turning on the projector and shining on a wall.

My Panasonic plasma blows away my very humble LG PA70G LED jobber in pretty much every measure except image size. That said, I still prefer to watch the projector most the time.

Then again, I paid about $2200 for the plasma over 7 years ago, and it was a steal then (average street price was about $3400-3700). The projector cost me $450, so it's pretty crazy to see just how close the image quality has gotten without even worrying about a bulb on the projector. It makes me want to wait out getting a nicer LED projector when they finally claw up a bit on the brightness level and get better resolution/optics at a reasonable price.

But like someone else said - it's apples to oranges comparing the two technologies. They have different strengths and weaknesses.